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On the formation and propagation of nonlinear internal boluses across a shelf break

Published online by Cambridge University Press:  19 April 2007

SUBHAS K. VENAYAGAMOORTHY  and
OLIVER B. FRINGER
SUBHAS K. VENAYAGAMOORTHY
Affiliation:
Environmental Fluids Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305-4020, USA
OLIVER B. FRINGER
Affiliation:
Environmental Fluids Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305-4020, USA
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Abstract

High-resolution two- and three-dimensional numerical simulations are performed of first-mode internal gravity waves interacting with a shelf break in a linearly stratified fluid. The interaction of nonlinear incident waves with the shelf break results in the formation of upslope-surging vortex cores of dense fluid (referred to here as internal boluses) that propagate onto the shelf. This paper primarily focuses on understanding the dynamics of the interaction process with particular emphasis on the formation, structure and propagation of internal boluses onshelf. A possible mechanism is identified for the excitation of vortex cores that are lifted over the shelf break, from where (from the simplest viewpoint) they essentially propagate as gravity currents into a linearly stratified ambient fluid.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 577 , 25 April 2007 , pp. 137 - 159
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Borzelli, G. & Ligi, R. 1999 Empirical orthogonal function analysis of sst image series: a physical interpretation. J. Phys. Oceanogr. 16, 682–690.Google Scholar
Cacchione, D. & Wunsch, C. 1974 Experimental study of internal waves over a slope. J. Fluid Mech. 66, 223–239.CrossRefGoogle Scholar
Carter, G. S., Gregg, M. C. & Lien, R.-C. 2005 Internal waves, solitary waves, and mixing on the Monterey Bay shelf. Continental Shelf Res. 25, 1499–1520.CrossRefGoogle Scholar
Craig, P. D. 1985 Internal wave dynamics over coastal topography. PhD thesis, University of Western Australia.Google Scholar
Cui, A. & Street, R. L. 2001 Large-eddy simulation of turbulent rotation convective flow development. J. Fluid Mech. 447, 53–84.CrossRefGoogle Scholar
Cui, A. & Street, R. L. 2004 Large-eddy simulation of coastal upwelling flow. Environ. Fluid Mech. 4, 197–223.CrossRefGoogle Scholar
Dauxois, T., Didier, A. & Falcon, E. 2004 Observation of near-critical reflection of internal waves in a stably stratified fluid. Phys. Fluids 16, 1936–1941.CrossRefGoogle Scholar
Dauxois, T. & Young, W. R. 1999 Near-critical reflection of internal waves. J. Fluid Mech. 390, 271–295.CrossRefGoogle Scholar
Fringer, O. B. & Street, R. L. 2003 The dynamics of breaking progressive interfacial waves. J. Fluid Mech. 494, 319–353.CrossRefGoogle Scholar
Hártel, C., Meiburg, E. & Necker, F. 2000 Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 418, 189–212.CrossRefGoogle Scholar
Ivey, G. N. & Nokes, R. I. 1989 Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204, 479–500.CrossRefGoogle Scholar
Ivey, G. N., Winters, K. B. & DeSilva, I. P. D. Silva, I. P. D. 2000 Turbulent mixing in a sloping benthic boundary layer energized by internal waves. J. Fluid Mech. 418, 59–76.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Klymak, J. M. & Moum, J. N. 2003 Internal solitary waves of elevation advancing on a shoaling shelf. Geophys. Res. Lett. 30, 2045.CrossRefGoogle Scholar
Kundu, P. K. 1990 Fluid Mechanics. Academic.Google Scholar
Kunze, E. & LlewellynSmith, S. G. Smith, S. G. 2004 The role of small-scale topography in turbulent mixing of the global ocean. Oceanography 17, 55–64.CrossRefGoogle Scholar
Legg, S. & Adcroft, A. 2003 Internal wave breaking at concave and convex continental slopes. J. Phys. Oceanogr. 33, 2224–2246.2.0.CO;2>CrossRefGoogle Scholar
Long, R. R. 1955 Some aspects of the flow of stratified fluids, III. Continuous density gradients. Tellus 7, 341–357.Google Scholar
Maxworthy, T., Leilich, J., Simpson, J. E. & Meiburg, E. 2002 The propagation of a gravity current into a linearly stratified fluid. J. Fluid Mech. 453, 371–394.CrossRefGoogle Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. 45, 1977–2010.CrossRefGoogle Scholar
Nash, J. D., Kunze, E., Toole, J. M. & Schmitt, R. W. 2004 Internal tide reflection and turbulent mixing on the continental slope. J. Phys. Oceanogr. 34, 1117–1134.2.0.CO;2>CrossRefGoogle Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
Simpson, A. E. 1972 Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 53, 759–768.CrossRefGoogle Scholar
Simpson, A. E. 1997 Gravity Currents. Cambridge University Press.Google Scholar
Simpson, A. E. & Britter, R. E. 1979 The dynamics of the head of a gravity current advancing over a horizontal surface. J. Fluid Mech. 94, 477–495.CrossRefGoogle Scholar
Slinn, D. N. & Riley, J. J. 1998 Turbulent dynamics of a critically reflecting internal gravity wave. Theor. Comput. Fluid Dyn. 11, 281–303.CrossRefGoogle Scholar
Taylor, J. R. 1993 Turbulence and mixing in the boundary layer generated by shoaling internal waves. J. Fluid Mech. 19, 233–233.Google Scholar
Thorpe, S. A. 1987 On the reflection of a strain of finite-amplitude internal waves from a uniform slope. J. Fluid Mech. 178, 279–302.CrossRefGoogle Scholar
Thorpe, S. A. 1992 Thermal fronts caused by internal gravity waves reflecting from a slope. J. Phys. Oceanogr. 22, 105–108.2.0.CO;2>CrossRefGoogle Scholar
Thorpe, S. A. 1999 The generation of alongslope currents by breaking internal waves. J. Phys. Oceanogr. 29, 29–45.2.0.CO;2>CrossRefGoogle Scholar
Ungarish, M. 2006 On gravity currents in a linearly stratified ambient: a generalization of Benjamin's steady-state propagation results. J. Fluid Mech. 548, 49–68.CrossRefGoogle Scholar
Venayagamoorthy, S. K. & Fringer, O. B. 2005 Nonhydrostatic and nonlinear contributions to the energy flux budget in nonlinear internal waves. Geophys. Res. Lett. 32, L15603.CrossRefGoogle Scholar
Venayagamoorthy, S. K. & Fringer, O. B. 2006 Numerical simulations of the interaction of internal waves with a shelf break. Phys. Fluids 18 (7), 076603.CrossRefGoogle Scholar
Zang, Y. & Street, R. L. 1995 Numerical simulation of coastal upwelling and interfacial instability in a rotating and stratified fluid. J. Fluid Mech. 305, 47–75.CrossRefGoogle Scholar
Zang, Y., Street, R. L. & Koseff, J. R. 1994 A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 18–33.CrossRefGoogle Scholar
Zedler, E. A. & Street, R. L. 2001 Large-eddy simulation of sediment transport: currents over ripples. J. Hydraul. Engng ASCE 127, 442–452.CrossRefGoogle Scholar